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Search: id:A099271
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| A099271 |
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Unsigned member r=-13 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 13, 196, 2925, 43681, 652288, 9740641, 145457325, 2172119236, 32436331213, 484372848961, 7233156403200, 108012973199041, 1612961441582413, 24086408650537156, 359683168316474925, 5371161116096586721
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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((-1)^(n+1))*a(n) = S_{-13}(n), n>=0, defined in A092184.
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= 2*(T(n, 15/2)-(-1)^n)/17, with twice Chebyshev's polynomials of the first kind evaluated at x=15/2: 2*T(n, 15/2)=A078365(n)=((15+sqrt(221))^n + (15-sqrt(221))^n)/2^n.
a(n)= 15*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 14*a(n-1) + 14*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=13.
G.f.: x*(1-x)/((1+x)*(1-15*x+x^2)) = x*(1-x)/(1-14*x-14*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
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Sequence in context: A159196 A015690 A027773 this_sequence A081796 A140536 A130549
Adjacent sequences: A099268 A099269 A099270 this_sequence A099272 A099273 A099274
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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